Harnett, Kristin E.
(2008)
On Duality and the Bi-Conjugate Gradient Algorithm.
Master's Thesis, University of Pittsburgh.
(Unpublished)
Abstract
It is not uncommon to encounter problems that lead to large, sparse linear systems with coefficient matrices that are invertible and sparse, but have little other structure. In such problems the solution u=A¹ƒ is typically calculated only to acurately compute functionals of the solution, L(u). This paper determines a method that converges rapidly to the functional's value. Specifially, a modified bi-conjugate gradient algorithm is found to generate convergence to the solution of linear functionals, L(u), much more rapidly than convergence to the linear system solution u.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
| Title | Member | Email Address | Pitt Username | ORCID |
|---|
| Committee Chair | Layton, William | wjl@pitt.edu | WJL | | | Committee Member | Rebholz, Leo | | | | | Committee Member | Sussman, Mike | | | |
|
| Date: |
28 September 2008 |
| Date Type: |
Completion |
| Defense Date: |
24 April 2008 |
| Approval Date: |
28 September 2008 |
| Submission Date: |
27 July 2008 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
MS - Master of Science |
| Thesis Type: |
Master's Thesis |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
bi-conjugate gradient; biconjugate gradient; duality; functionals; iterative methods; sparse systems |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-07272008-001302/, etd-07272008-001302 |
| Date Deposited: |
10 Nov 2011 19:54 |
| Last Modified: |
15 Nov 2016 13:47 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/8654 |
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